Finite Group Databasebeta

← #21459812

Subgroups — #21459812

Order 7808.

1012 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840488C211yesmaximal, characteristic, complemented
2#16840484C213yesmaximal, complemented
3#16840467C213yesmaximal, complemented
4#16840460C213yesmaximal, complemented
5#16840453C213yesmaximal, complemented
6Q8×C22⋊D61C211yesmaximal, characteristic, complemented
7#16840424C211yesmaximal, characteristic, complemented
8#16840423C211yesmaximal, characteristic, complemented
9#16840384C213yesmaximal, complemented
10#16840370C213yesmaximal, complemented
11#16840296C213yesmaximal, complemented
12#16840296C213yesmaximal, complemented
13#16840244C211yesmaximal, characteristic, complemented
14#16840238C211yesmaximal, characteristic, complemented
15C2×C4×Q8×C61C211yesmaximal, characteristic, complemented
16C2×#11758226C2211yescharacteristic
17C2×Q8×D61C2211yescharacteristic
18#14519776C2213yes—
19#14519775C2213yes—
20#14519772C2216yes—
21#14519771C2213yes—
22#14519771C2213yes—
23#14519771C2216yes—
24#14519769C2213yes—
25#14519769C2213yes—
26#14519768C2213yes—
27#14519767C2216yes—
28#14519766C2213yes—
29#14519765C2213yes—
30#14519765C2213yes—
31#14519762C2216yes—
32#14519760C2211yescharacteristic
33#14519760C2213yes—
34#14519757C2213yes—
35#14519756C2213yes—
36#14519756C2213yes—
37#14519755C2216yes—
38#14519753C2213yes—
39#14519753C2213yes—
40#14519752C2213yes—
41#14519751C2213yes—
42#14519751C2213yes—
43Q8×Dic61C2211yescharacteristic
44Q8×Dic61C2211yescharacteristic
45C4×Dic122C2213yes—
46C4×Dic122C2213yes—
47#14519742C2213yes—
48C4×D244C2213yes—
49C4×D244C2213yes—
50#14519739C2213yes—
51C4×C22⋊D61C2216yes—
52C4×C22⋊D61C2213yes—
53C4×C22⋊D61C2213yes—
54#14519735C2213yes—
55#14519734C2216yes—
56#14519734C2213yes—
57#14519734C2213yes—
58C4⋊C4×D61C2213yes—
59C22×Q8×C61C2211yescharacteristic
60C4×Q8×C61C2213yes—
61C4×Q8×C61C2211yescharacteristic
62C4×Q8×C61C2211yescharacteristic
63C4×Q8×C61C2213yes—
64C2×C4⋊C4×C61C2213yes—
65C2×C42×C61C2213yes—
66C2×Q8×C61—24no—
67C2×Q8×C61C2313yes—
68C2×Q8×C61C2311yescharacteristic
69C22×C4×C61C2311yescharacteristic
70C22×C4×C61C2313yes—
71C22×C4×C61C2313yes—
72C2×C22⋊D61C2313yes—
73C2×C22⋊D61C2311yescharacteristic
74#11758226—24no—
75Q8×D61—24no—
76C2×D244C2313yes—
77C2×D244C2313yes—
78C2×C4×D61C2313yes—
79C2×C4×D61C2313yes—
80C2×C4×D61C2316yes—
81C2×Dic122C2313yes—
82C2×Dic122C2313yes—
83C4⋊C4×C61C2313yes—
84C4⋊C4×C61C2313yes—
85C4⋊C4×C61C2316yes—
86C42×C61C2313yes—
87C42×C61C2313yes—
88C42×C61C2313yes—
89C42×C61C2313yes—
90C22⋊Dic61C2311yescharacteristic
91C22⋊Dic61C2313yes—
92#11758198C2311yescharacteristic
93#11758198C2313yes—
94#11758198C2313yes—
95#11758198C2313yes—
96#11758198C2313yes—
97#11758198C2316yes—
98#11758198C2316yes—
99#11758198C2313yes—
100#11758198C2313yes—
101#11758198C2311yescharacteristic
102C4⋊Dic61C2313yes—
103C4⋊Dic61C2313yes—
104C4⋊Dic61C2313yes—
105C4⋊Dic61C2313yes—
106#11758196C2313yes—
107#11758196C2311yescharacteristic
108#11758196C2313yes—
109#11758196C2313yes—
110#11758196C2313yes—
111#11758196C2316yes—
112#11758196C2313yes—
113#11758196C2316yes—
114#11758196C2313yes—
115#11758196C2311yescharacteristic
116C4×Dic61C2316yes—
117C4×Dic61C2313yes—
118C4×Dic61C2313yes—
119C23×C61C2411yescharacteristic
120C22×D61C2411yescharacteristic
121C22×D61C2413yes—
122Q8×C61—26no—
123Q8×C61#4114yes—
124C2×C4×C61—22no—
125C2×C4×C61—26no—
126C2×C4×C61—43no—
127C2×C4×C61C2413yes—
128C2×C4×C61C2411yescharacteristic
129C2×C4×C61C2411yescharacteristic
130C2×C4×C61C2413yes—
131C2×C4×C61C2413yes—
132C2×C4×C61C2413yes—
133C22⋊D61—26no—
134C22⋊D61—22no—
135C2×Dic61C2413yes—
136C2×Dic61C2411yescharacteristic
137C2×Dic61C2411yescharacteristic
138C2×Dic61C2413yes—
139C2×Dic61C2413yes—
140C2×Dic61C2411yescharacteristic
141D244—26no—
142D244—43no—
143C4×D61—26no—
144C4×D61—26no—
145C4×D61—46no—
146Dic122—26no—
147Dic122—43no—
148C22×C61—21no—
149C22×C61—21no—
150C22×C612−1+412yes—
151C22×C61C2511yescharacteristic
152C2×D61—21no—
153C2×D61—23no—
154C2×D61—21no—
155C2×D61—23no—
156C2×D61—23no—
157C2×D61—21no—
158C4×C61—23no—
159C4×C61—21no—
160C4×C61—21no—
161C4×C61—23no—
162C4×C61—23no—
163C4×C61C2×#4116yes—
164Dic61—23no—
165Dic61—21no—
166Dic61—23no—
167Dic61—21no—
168Dic61—21no—
169Dic61—23no—
170#3516—611nomaximal, Sylow
171C2×C61—22no—
172C2×C61C22×#4111yescharacteristic
173C2×C61C2×2−1+411yescharacteristic
174C2×C61#58511yescharacteristic
175D61—41no—
176D61—43no—
177#557—611no—
178#556—613no—
179#554—613no—
180#553—613no—
181#552—613no—
182D4×Q8—611no—
183#548—611no—
184#548—611no—
185#542—613no—
186#541—613no—
187#529—613no—
188#529—613no—
189#520—611no—
190#519—611no—
191C2×C4×Q8D6111yescharacteristic, complemented
192C61#351611yescharacteristic, complemented, Sylow
193C2×#41—611no—
194C22×Q8—611no—
195C22×Q8C2×D6111yescharacteristic
196C4⋊Q8—613no—
197C4⋊Q8—613no—
198#126—616no—
199#126—616no—
200#126—613no—
201#126—613no—
202#125—616no—
203#125—613no—
204#125—613no—
205#125—613no—
206#124—613no—
207#124—613no—
208#124—613no—
209#123—611no—
210#123—613no—
211#123—616no—
212C22⋊Q8—613no—
213C22⋊Q8—613no—
214C22⋊Q8—613no—
215C22⋊Q8—613no—
216C22⋊Q8—613no—
217C22⋊Q8—616no—
218#121—613no—
219#121—613no—
220#121—613no—
221C4×Q8—611no—
222C4×Q8—611no—
223C4×Q8—613no—
224C4×Q8—613no—
225C4×Q8—613no—
226C4×Q8C2×D6111yescharacteristic
227C4×Q8C2×D6113yes—
228C4×Q8C2×D6111yescharacteristic
229C4×Q8C2×D6113yes—
230C4×D4—613no—
231C4×D4—613no—
232C4×D4—616no—
233C4×D4—613no—
234C4×D4—613no—
235C4×D4—613no—
236#117—613no—
237#117—613no—
238#117—613no—
239#117—616no—
240C2×C4⋊C4—613no—
241C2×C4⋊C4C2×D6113yes—
242C2×C42C2×D6113yes—
243#41—1224no—
244C2×Q8—24no—
245C2×Q8—613no—
246C2×Q8—613no—
247C2×Q8—1224no—
248C2×Q8C22×D6113yes—
249C2×Q8C22×D6111yescharacteristic
250C2×D4—613no—
251C2×D4—611no—
252C2×D4—613no—
253C2×D4—613no—
254C22×C4—613no—
255C22×C4—613no—
256C22×C4—616no—
257C22×C4C22×D6111yescharacteristic
258C22×C4C22×D6113yes—
259C22×C4C22×D6113yes—
260C4⋊C4—613no—
261C4⋊C4—613no—
262C4⋊C4—611no—
263C4⋊C4—613no—
264C4⋊C4—613no—
265C4⋊C4—613no—
266C4⋊C4—616no—
267C4⋊C4—613no—
268C4⋊C4—616no—
269C4⋊C4—613no—
270C4⋊C4—611no—
271C4⋊C4—613no—
272C4⋊C4—613no—
273C4⋊C4—613no—
274C4⋊C4C22×D6113yes—
275C4⋊C4C22×D6113yes—
276C4⋊C4C22×D6116yes—
277C22⋊C4—611no—
278C22⋊C4—613no—
279C22⋊C4—613no—
280C22⋊C4—611no—
281C22⋊C4—613no—
282C22⋊C4—613no—
283C22⋊C4—613no—
284C22⋊C4—616no—
285C22⋊C4—611no—
286C22⋊C4—616no—
287C22⋊C4—613no—
288C22⋊C4—613no—
289C42—616no—
290C42—613no—
291C42—613no—
292C42C22×D6113yes—
293C42C22×D6113yes—
294C42C22×D6113yes—
295C42C22×D6113yes—
296C23—611no—
297C23—613no—
298C23C23×D6111yescharacteristic
299Q8—26no—
300Q8—1226no—
301Q8—2443no—
302Q8#1175822214yes—
303D4—1226no—
304D4—1222no—
305D4—1226no—
306D4—2443no—
307C2×C4—22no—
308C2×C4—26no—
309C2×C4—43no—
310C2×C4—611no—
311C2×C4—613no—
312C2×C4—611no—
313C2×C4—613no—
314C2×C4—613no—
315C2×C4—611no—
316C2×C4—1226no—
317C2×C4—1226no—
318C2×C4—2446no—
319C2×C4C23×D6113yes—
320C2×C4C23×D6111yescharacteristic
321C2×C4C23×D6111yescharacteristic
322C2×C4C23×D6113yes—
323C2×C4C23×D6113yes—
324C2×C4C23×D6113yes—
325C22—21no—
326C22—21no—
327C22—1221no—
328C22—1223no—
329C22—1221no—
330C22—1223no—
331C22—1223no—
332C22—1221no—
333C22#1451982512yes—
334C22C24×D6111yescharacteristic
335C4—23no—
336C4—21no—
337C4—21no—
338C4—23no—
339C4—23no—
340C4—1221no—
341C4—1223no—
342C4—1223no—
343C4—1221no—
344C4—1223no—
345C4—1221no—
346C4C2×#1175822216yes—
347C2—22no—
348C2—2441no—
349C2—2443no—
350C2C22×#1175822211yescharacteristic
351C2C2×#1451982511yescharacteristic
352C2#1684059811yescharacteristic
subgroupG/H
center, FrattiniC22C24×D61
commutator, socleC22×C61C25
FittingC2×C4×Q8×C61C2
hypercenterC2×C4×Q8D61
hypocenterC61#3516
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4×Q8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #16840488C2semidirect
2. #16840484C2semidirect
3. #16840467C2semidirect
4. #16840460C2semidirect
5. #16840453C2semidirect
6. Q8×C22⋊D61C2semidirect
7. #16840424C2semidirect
8. #16840423C2semidirect
9. #16840384C2semidirect
10. #16840370C2semidirect
11. #16840296C2semidirect
12. #16840296C2semidirect
13. #16840244C2semidirect
14. #16840238C2semidirect
15. C2×C4×Q8×C61C2semidirect
191. C2×C4×Q8D61semidirect
192. C61#3516semidirect